Rambam lived safely in Egypt. If I remember correctly, Ashkenzi rabbonim poskened that Christianity is “shituf” – not avodah zarah but saying that there is something in addition to HKBH. Quite understandable, especially if you lived in a Catholic country where the local rabbi could be called on to debate priests in the public square. In any case, that’s how it’s poskened today. About non-mainline groups like J’s Witnesses or Mormons I’m not sure. Most of the Christians I know try to be good people according to their understanding, even if some of them do believe some strange things about Jews. (The Jews own all the banks? I’m a Jew – where’s my bank? I want my bank! 🙂 I assume the same is true for most Muslims outside the anti-Israel groups.
I think the kosher-halal question might depend upon whether halal is available in a given area, or a Muslim might have to make do with kosher. At least he’s sure there are no non-halal animal products in it.